All parts please

3. (30 points) (a) Find the absolute and relative errors in approximating the exact value a = 4 with g =42, (b) Determine the relative condition number &, (f,z) for evaluating the value of flz)=cosx at x = w/3. (Hint: sinw/3 = /3/2 and cos7/3 = 1/2.) , ) o L ) rmx () In Problem 3b, suppose @ = 7/3 is changed to & with a relative error |||| = , x where > 0 is a sufficiently small number. Let y = f(2) = cos&. Estimate the relative forward error . 9 vl lyl based on the backward error and the relative condition number x.(f,x) at = a